Xun (Ryan) Huan

Assistant Professor

Xun (Ryan) Huan is an Assistant Professor of Mechanical Engineering at
the University of Michigan. Prior to U-M, he was a postdoctoral
researcher at Sandia National Laboratories in Livermore, California.
His research broadly revolves around uncertainty quantification,
machine learning, and numerical optimization. He is particularly
interested in optimal experimental design, Bayesian analysis,
multilevel and multifidelity methods, model misspecification, and
scientific computing. Outside work, Xun is passionate about aviation
and holds a private pilot certificate.

Research

Optimal Experimental Design

Experiments are often expensive, time-consuming, and perhaps even
dangerous. However, not all experiments are equal, and some can
produce more valuable data than others. Identifying and executing
these “good” experiments can lead to substantial resource savings.

We develop mathematical frameworks and computational algorithms for
optimal experimental design (OED), and seek to address questions such
as:

Under what condition should we conduct an experiment?

What quantities should we probe?

Where and when should we take measurements?

Have we gathered enough data and should stop, or continue with more experiments?

OED is a form of decision-making under uncertainty. For example,
when our experimental goal is to learn about model parameters from
noisy measurements, a possible approach involves finding the design
decision maximizing the expected information gain (mutual
information).

There are many challenges associated with finding the optimal design,
including the need for optimization routines to accommodate noisy
responses, repeated Bayesian inferences under different scenarios, and
all while wrapping around an often computationally intensive and
highly nonlinear physics-based forward model with high-dimensional
input and output spaces.

Example: hydrogen-oxygen ignition

Design: initial temperature and equivalence ratio

Measure: ignition delay times

Infer: Arrhenius kinetic parameters

Below are expected utility contours approximated from using the full
physical model (left), and a polynomial chaos surrogate model that
greatly accelerate the computations (right); they show excellent
agreement.

With full model

With polynomial chaos surrogate model

Three experiments are simulated (at designs A, B, and C in figure
above). Bayesian inference is performed and posterior densities are
shown below. Designs A (which has the highest expected utility value)
produces the “tightest” posterior (left), reflecting a larger
reduction in uncertainty and increased confidence for estimating these
parameters.

Design A

Design B

Design C

Sequential Experimental Design

Coming soon!

Uncertainty Quantification for Machine Learning

Coming soon!

Uncertainty Quantification in Engineering Applications

Uncertainty quantification (UQ) plays a crucial role in engineering
and science. It enters research and production workflows at various
points, such as the highlighted yellow fields below. UQ is
particularly important for the learning process, by providing a
principled framework for interactions among theory, models, and data.

Example: reactive flows inside a scramjet combustor

Scramjets are propulsive systems that can enable efficient and stable
operations under hypersonic flight conditions (Mach 5+). For instance,
the figure below shows the flight test payload from the Hypersonic
International Flight Research Experimentation (HIFiRE) program.

Designing scramjet engines requires both accurate flow simulations as
well as UQ. Enabling UQ for expensive simulations of turbulent
supersonic reactive flows faces many computational
challenges. Techniques such as global sensitivity analysis, surrogate
modeling, compressive sensing, efficient Bayesian calibration, and
multilevel multifidelity sampling are needed to make UQ analysis
possible. Below is an illustration of the predictive uncertainty (blue
contours) of Mach number at select vertical stations of the combustor
section. Such information would be valuable for finding optimal
scramjet designs that are also robust and reliable.